Annealing networks and fractal landscapes

Abstract

The conventional explanation for the poor scaling of Hopfield and Tank networks is that they have difficulty in balancing the tradeoff between the path length and the legality components of the energy function. An experiment is described which suggests that the conventional explanation is either wrong, or, at best, incomplete. An alternative explanation is proposed, i.e., that these networks might scale better if their dynamics effectively implemented a divide-and-conquer strategy, if they recursively decomposed the problem into smaller independent subproblems. An annealing network can do so if the energy landscape has a self-similar quasi-fractal structure. It is the author's belief that this proposition applies to both discrete and analog networks. His proposition is supported by describing his work in finding low-cost solutions for traveling salesman problems. The implications for two other optimization problems (graph bisection and coloring) are considered. >